Do people in Canada, central and South America get annoyed by the US calling itself 'America'?

I do, and I'm British. I live in the UK - the united kingdom of great britain and northern ireland (the lack of capital letters is intentional) - and I should point out [in case anyone wants to pick a fight] that the 'great' in 'Great Britain' is only there to distinguish it from the (now) French Brittany - and means larger, rather than mighty.
I'm not at all anti USA. In fact I love the country.

But how many people in the US are thinking of Venezuela when 'God Bless America' is sung?
And does 'My fellow Americans' include Chileans?

Canada is not an extension of the US!

I live in the U.S. of A.

my ex-girlfriend hated it when I called the U.S. America.

I've tried persuading Canadians that they shouldn't let the USA get away with hi-jacking the entire continent in this way, but they don't seem to be at all resentful of the fact. In Central and South America the position is different, as when you use the name "America" in Spanish it refers to their part of the world and when they refer to the United States they always call them just that.

That would be childish. U.S. ctizens ARE Americans.

Most American I know refer to their country as USA, it is mostly Europeans (incl UK) that refer to it as America

I'll be sure to call my fellow citizens "United States of Americans", instead of their ***well known shorthand name***, just to please you.

Most people don't identify themselves as "North American" or "South American". If they are from Canada, they are in North America but they are Canadians. If you are in Venezuela, you are Venezuelan. Americans are citizens with the only country that has the word America in it's name and are therefore American, not United States of Americans.